球楔台球：从混沌到分形和塔尔博特地毯
Spherical wedge billiard: from chaos to fractals and Talbot carpets
摘要：
我们介绍了球楔台球，一个动力系统，由一个粒子沿测地线上的一个封闭的非欧表面的球楔。我们推导出相应的庞加莱映射的解析形式，并发现非常复杂的动力学，从完全混沌到非常规则，表现出分形特征。此外，我们表明，在改变台球参数，庞加莱映射的不动点合并在复杂的方式，这有起源于台球映射的球差。我们还详细分析了相空间图与Talbot地毯密切相关时的规则区域。
英文摘要：
We introduce the spherical wedge billiard, a dynamical system consisting of a particle moving along a geodesic on a closed non-Euclidean surface of a spherical wedge. We derive the analytic form of the corresponding Poincaré map and find very complex dynamics, ranging from completely chaotic to very regular, exhibiting fractal features. Further, we show that upon changing the billiard parameter, the fixed points of the Poincaré map merge in complex ways, which has origin in the spherical aberration of the billiard mapping. We also analyze in detail the regular regime when phase space diagram is closely related to Talbot carpets.
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